Set Theory
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Set Theory
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Author : Abhijit Dasgupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Set Theory written by Abhijit Dasgupta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.
Set Theory
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Author : Andras Hajnal
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-11
Set Theory written by Andras Hajnal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-11 with Mathematics categories.
This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.
Set Theory
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Author : Thomas Jech
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-23
Set Theory written by Thomas Jech and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-23 with Mathematics categories.
This monograph covers the recent major advances in various areas of set theory. From the reviews: "One of the classical textbooks and reference books in set theory....The present ‘Third Millennium’ edition...is a whole new book. In three parts the author offers us what in his view every young set theorist should learn and master....This well-written book promises to influence the next generation of set theorists, much as its predecessor has done." --MATHEMATICAL REVIEWS
Set Theory Of The Continuum
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Author : Haim Judah
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Set Theory Of The Continuum written by Haim Judah and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin.
Set Theory And Its Logic
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Author : Willard Van Orman Quine
language : en
Publisher: Harvard University Press
Release Date : 1969
Set Theory And Its Logic written by Willard Van Orman Quine and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
This is an extensively revised edition of W. V. Quine’s introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
Set Theory An Introduction
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Author : Robert L. Vaught
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-28
Set Theory An Introduction written by Robert L. Vaught and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-28 with Mathematics categories.
By its nature, set theory does not depend on any previous mathematical knowl edge. Hence, an individual wanting to read this book can best find out if he is ready to do so by trying to read the first ten or twenty pages of Chapter 1. As a textbook, the book can serve for a course at the junior or senior level. If a course covers only some of the chapters, the author hopes that the student will read the rest himself in the next year or two. Set theory has always been a sub ject which people find pleasant to study at least partly by themselves. Chapters 1-7, or perhaps 1-8, present the core of the subject. (Chapter 8 is a short, easy discussion of the axiom of regularity). Even a hurried course should try to cover most of this core (of which more is said below). Chapter 9 presents the logic needed for a fully axiomatic set th~ory and especially for independence or consistency results. Chapter 10 gives von Neumann's proof of the relative consistency of the regularity axiom and three similar related results. Von Neumann's 'inner model' proof is easy to grasp and yet it prepares one for the famous and more difficult work of GOdel and Cohen, which are the main topics of any book or course in set theory at the next level.
Set Theory With Applications
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Author : Shwu-Yeng T. Lin
language : en
Publisher: Mancorp Publishing
Release Date : 1985
Set Theory With Applications written by Shwu-Yeng T. Lin and has been published by Mancorp Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Elements Of Set Theory
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Author : Herbert B. Enderton
language : en
Publisher: Academic Press
Release Date : 1977-05-23
Elements Of Set Theory written by Herbert B. Enderton and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-05-23 with Mathematics categories.
This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Axiomatic Set Theory
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Author : Patrick Suppes
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04
Axiomatic Set Theory written by Patrick Suppes and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Mathematics categories.
Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
Axiomatic Set Theory Part 2
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Author : Thomas J. Jech
language : en
Publisher: American Mathematical Soc.
Release Date : 1971
Axiomatic Set Theory Part 2 written by Thomas J. Jech and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Axiomatic set theory categories.